The Egypt international has not played a competitive match for the Gunners this season and made just eight Premier League appearances in the previous campaign.
I am very excited to be joining Turkish giants Besiktas and I look forward to achieving our targets in the Super Lig and Europe. 🦅— Mohamed ELNeny (@ElNennY) August 31, 2019
To my dear Arsenal fans and team mates ,i wish all the success for the season and be sure that i will be following the teams progress from Istanbul pic.twitter.com/DXl0SdEAW2
Arsenal head coach Unai Emery strengthened his midfield options with the signing of Dani Ceballos on loan from Real Madrid in July, so has allowed Elneny to move to the Turkish Super Lig to get more game time.
Elneny was signed by former Arsenal boss Arsene Wenger from Swiss side Basel in January 2016.
The 27-year-old signed a long-term contract with the Gunners in March 2018, with that deal reportedly running to 2022.